I really like Chet's playing on "Solo Flights" and "Me and my guitar". Two of my favourite albums; especially "Solo Flights". Does anyone know which acoustic guitar he used to record these albums?

The guitar sounds a bit like his classical electric, however that is impossible because the CE was introduced in 1981 if I'm correct. This for example sounds a bit like it was recorded with his electric classical https://www.youtube.com/watch?v=4iYdBBw-X88

Now, for some facts: At this time, Chet recorded quite a bit with an an Estruch classic fitted with a Baldwin Prismatone pickup. (He used this on Struttin', from the same LP.) Chet used many mics during his career, but he is on record as saying that he liked the Neumann KM84 for recording classicals. This mic was readily available during this time (mid/late 1970's), so I would vote for a combination of Estruch with Prismatone, and one or more KM84 mic(s). Of course, there is some very nice EQ and reverb, possibly EMT plate reverb- the real deal.